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Semi-Lagrangian off-lattice Boltzmann method for weakly compressible flows

Andreas Krämer1,*, Knut Küllmer1,†, Dirk Reith1,‡, Wolfgang Joppich1,§, and Holger Foysi2,¶

  • 1Institute for Technology, Renewables and Energy-efficient Engineering (TREE), Bonn-Rhein-Sieg University of Applied Sciences, Grantham-Allee 20, 53757 Sankt Augustin, Germany
  • 2Department of Mechanical Engineering, University of Siegen, Paul-Bonatz-Straße 9-11, 57076 Siegen-Weidenau, Germany

  • *andreas.kraemer@h-brs.de; kraemer.research@gmail.com
  • †knut.kuellmer@h-brs.de
  • ‡dirk.reith@h-brs.de; Also at Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Schloss Birlinghoven, 53754 Sankt Augustin, Germany.
  • §wolfgang.joppich@h-brs.de
  • holger.foysi@uni-siegen.de
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Phys. Rev. E 95, 023305 – Published 3 February, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.023305

Abstract

The lattice Boltzmann method is a simulation technique in computational fluid dynamics. In its standard formulation, it is restricted to regular computation grids, second-order spatial accuracy, and a unity Courant-Friedrichs-Lewy (CFL) number. This paper advances the standard lattice Boltzmann method by introducing a semi-Lagrangian streaming step. The proposed method allows significantly larger time steps, unstructured grids, and higher-order accurate representations of the solution to be used. The appealing properties of the approach are demonstrated in simulations of a two-dimensional Taylor-Green vortex, doubly periodic shear layers, and a three-dimensional Taylor-Green vortex.

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References (47)

  1. G. R. McNamara and G. Zanetti, Phys. Rev. Lett. 61, 2332 (1988).
  2. F. J. Higuera, S. Succi, and R. Benzi, Europhys. Lett. 9, 345 (1989).
  3. C. K. Aidun and J. R. Clausen, Annu. Rev. Fluid Mech. 42, 439 (2010).
  4. B. Dünweg and A. J. C. Ladd, in Advanced Computer Simulation Approaches for Soft Matter Sciences, Advanced Polymer Science Vol. 221, edited by P. G. Bolhuis (Springer, Berlin, 2009), pp. 89–166.
  5. A. Mazloomi M, S. S. Chikatamarla, and I. V. Karlin, Phys. Rev. Lett. 114, 174502 (2015).
  6. S. S. Chikatamarla, C. E. Frouzakis, I. V. Karlin, A. G. Tomboulides, and K. B. Boulouchos, J. Fluid Mech. 656, 298 (2010).
  7. L. Jahanshaloo, E. Pouryazdanpanah, and N. A. Che Sidik, Numer. Heat Tr. A-Appl. 64, 938 (2013).
  8. I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302 (2014).
  9. M. Namburi, S. Krithivasan, and S. Ansumali, Sci. Rep. 6, 27172 (2016).
  10. A. Fakhari and T. Lee, Comput. Fluids 107, 205 (2015).
  11. K. Hejranfar and E. Ezzatneshan, J. Comput. Phys. 267, 28 (2014).
  12. F. Nannelli and S. Succi, J. Stat. Phys. 68, 401 (1992).
  13. H. Xi, G. Peng, and S.-H. Chou, Phys. Rev. E 59, 6202 (1999).
  14. D. V. Patil and K. N. Lakshmisha, J. Comput. Phys. 228, 5262 (2009).
  15. S. Ubertini and S. Succi, Commun. Comput. Phys. 3, 342 (2008).
  16. A. Düster, L. Demkowicz, and E. Rank, Int. J. Numer. Meth. Eng. 67, 1094 (2006).
  17. Y. Li, E. LeBoeuf, and P. Basu, Phys. Rev. E 72, 046711 (2005).
  18. A. Zadehgol, M. Ashrafizaadeh, and S. H. Musavi, Comput. Fluids 105, 58 (2014).
  19. M. Min and T. Lee, J. Comput. Phys. 230, 245 (2011).
  20. A. Krämer, D. Wilde, N. Zawadzki, K. Küllmer, D. Reith, W. Joppich, and H. Foysi (unpublished).
  21. A. Krämer, D. Wilde, K. Küllmer, D. Reith, H. Foysi, and W. Joppich (unpublished).
  22. M. A. Heroux, R. A. Bartlett, V. E. Howle, R. J. Hoekstra, J. J. Hu, T. G. Kolda, R. B. Lehoucq, K. R. Long, R. P. Pawlowski, E. T. Phipps, A. G. Salinger, H. K. Thornquist, R. S. Tuminaro, J. M. Willenbring, A. Williams, and K. S. Stanley, ACM Trans. Math. Softw. 31, 397 (2005).
  23. T. Lee and C.-L. Lin, J. Comput. Phys. 185, 445 (2003).
  24. M. Falcone and R. Ferretti, Semi-Lagrangian Approximation Schemes for Linear and Hamilton—Jacobi Equations (Society for Industrial and Applied Mathematics, Philadelphia, 2013).
  25. C. Shu, X. D. Niu, and Y. T. Chew, Phys. Rev. E 65, 036708 (2002).
  26. M. Cheng and K. C. Hung, Int. J. Comput. Eng. Sci. 05, 291 (2004).
  27. A. Bardow, I. V. Karlin, and A. A. Gusev, Europhys. Lett. 75, 434 (2006).
  28. P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 (1954).
  29. Y. H. Qian, D. D'Humières, and P. Lallemand, Europhys. Lett. 17, 479 (1992).
  30. I. V. Karlin, A. Ferrante, and H. C. Öttinger, Europhys. Lett. 47, 182 (1999).
  31. P. Lallemand and L.-S. Luo, Phys. Rev. E 61, 6546 (2000).
  32. J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods (Springer, New York, 2008), Vol. 54.
  33. W. Bangerth, R. Hartmann, and G. Kanschat, ACM Trans. Math. Softw. 33, 24 (2007).
  34. D. L. Brown, J. Comput. Phys. 122, 165 (1995).
  35. M. L. Minion and D. L. Brown, J. Comput. Phys. 138, 734 (1997).
  36. P. J. Dellar, J. Comput. Phys. 190, 351 (2003).
  37. M. V. Lipavskii, A. I. Tolstykh, and E. N. Chigirev, Comp. Math. Math. Phys. 53, 296 (2013).
  38. F. Bösch, S. S. Chikatamarla, and I. Karlin, ESAIM: Proc. Surv. 52, 1 (2015).
  39. M. E. Brachet, D. I. Meiron, S. A. Orszag, B. G. Nickel, R. H. Morf, and U. Frisch, J. Fluid Mech. 130, 411 (1983).
  40. G. J. Gassner and A. D. Beck, Theor. Comput. Fluid Dyn. 27, 221 (2013).
  41. F. S. Schranner, J. A. Domaradzki, S. Hickel, and N. A. Adams, Comput. Fluids 114, 84 (2015).
  42. H. Foysi and S. Sarkar, Theor. Comput. Fluid Dyn. 24, 565 (2010).
  43. C. Pantano and S. Sarkar, J. Fluid Mech. 451, 329 (2002).
  44. J. DeBonis, in 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition (American Institute of Aeronautics and Astronautics, Chicago, IL, 2013).
  45. M. Junk, A. Klar, and L.-S. Luo, J. Comput. Phys. 210, 676 (2005).
  46. D. J. Holdych, D. R. Noble, J. G. Georgiadis, and R. O. Buckius, J. Comput. Phys. 193, 595 (2004).
  47. X. Shi, J. Lin, and Z. Yu, Int. J. Numer. Meth. Fl. 42, 1249 (2003).

Outline

Information

Phys. Rev. E 95, 023305– Published 3 February, 2017
  • Received 27 September 2016
  • Revised 21 November 2016

©2017 American Physical Society

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